Finite Group Databasebeta

← #19134414

Subgroups — #19134414

Order 5504.

332 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063290C211yesmaximal, characteristic
2C2×#13063250C211yesmaximal, characteristic
3C2×#13063248C211yesmaximal, characteristic
4C2×C8×Dic43C211yesmaximal, characteristic
5C4⋊C4×Dic43C211yesmaximal, characteristic
6#14582661C211yesmaximal, characteristic
7C43×#340C211yesmaximal, characteristic
8C22×Dic86C2211yescharacteristic
9C22×C43⋊C8C2211yescharacteristic
10#13063290—22no—
11#13063290C414yescomplemented
12C2×C4⋊Dic43C2211yescharacteristic
13C2×Dic43⋊C4—21no—
14C2×C4×Dic43—21no—
15C2×C4×Dic43—21no—
16C2×C4×Dic43C2211yescharacteristic
17#13063250C414yescomplemented
18#13063248C414yescomplemented
19C8×Dic43—22no—
20C43⋊#95—21no—
21C22×C8×C43C2211yescharacteristic
22C2×C4⋊C4×C43C2211yescharacteristic
23C2×C4⋊C4×C43C2211yescharacteristic
24C22×C4×C43—21no—
25C22×C4×C43—21no—
26C22×C4×C43C2311yescharacteristic
27C22×Dic43—21no—
28C22×Dic43—21no—
29C22×Dic43D411yescharacteristic
30C22×Dic43D411yescharacteristic
31C2×Dic86—21no—
32C2×Dic86—21no—
33C2×Dic86—21no—
34C2×Dic86C2×C412yes—
35C2×Dic86C2×C412yes—
36C2×Dic86C2×C412yes—
37C2×C8×C43—21no—
38C2×C8×C43—21no—
39C2×C8×C43C2×C412yes—
40C4⋊C4×C43—21no—
41C4⋊C4×C43—21no—
42C4⋊C4×C43C2×C412yes—
43C4⋊C4×C43C2×C412yes—
44C4⋊Dic43—21no—
45C4⋊Dic43C2×C412yes—
46Dic43⋊C4—24no—
47C4×Dic43—24no—
48C4×Dic43—42no—
49C4×Dic43C2×C412yes—
50C4×Dic43D412yes—
51C2×C43⋊C8—21no—
52C2×C43⋊C8—21no—
53C2×C43⋊C8C2×C412yes—
54C23×C43C2×D411yescharacteristic
55C2×C4×C43—22no—
56C2×C4×C43—22no—
57C2×C4×C43—41no—
58C2×C4×C43—41no—
59C2×C4×C43—41no—
60C2×C4×C43—41no—
61C2×C4×C43C22×C411yescharacteristic
62C2×C4×C43C22×C411yescharacteristic
63C2×C4×C43C22×C411yescharacteristic
64C2×C4×C43C2×D411yescharacteristic
65C2×C4×C43#4111yescharacteristic
66C2×C4×C43#4111yescharacteristic
67C2×Dic43—22no—
68C2×Dic43—22no—
69C2×Dic43—22no—
70C2×Dic43—21no—
71C2×Dic43—21no—
72C2×Dic43—22no—
73C2×Dic43—41no—
74C2×Dic43—41no—
75C2×Dic43C22⋊C412yes—
76C2×Dic43C22⋊C412yes—
77C2×Dic43SD1612yes—
78C2×Dic43Q1612yes—
79Dic86—22no—
80Dic86—22no—
81Dic86—22no—
82Dic86C4214yescomplemented
83C8×C43—22no—
84C43⋊C8—22no—
85C22×C43C2×C22⋊C411yescharacteristic
86C22×C43C4×D411yescharacteristic
87C22×C43C4×D411yescharacteristic
88C22×C43C2×SD1611yescharacteristic
89C22×C43C2×Q1611yescharacteristic
90C22×C43#13511yescharacteristic
91C22×C43#13511yescharacteristic
92C4×C43—42no—
93C4×C43—42no—
94C4×C43C2×C4211yescharacteristic
95C4×C43#11711yescharacteristic
96C4×C43C4×D411yescharacteristic
97C4×C43C4×D411yescharacteristic
98Dic43—24no—
99Dic43—22no—
100Dic43—42no—
101Dic43#10314yescomplemented
102C4×#103—431nomaximal, Sylow
103C2×C43C4×C22⋊C411yescharacteristic
104C2×C43C2×#10311yescharacteristic
105C2×C43#41611yescharacteristic
106C2×C43C4×SD1611yescharacteristic
107C2×C43C4×SD1611yescharacteristic
108C2×C43C4×Q1611yescharacteristic
109C2×C43C4×Q1611yescharacteristic
110C2×C4×Q8—431no—
111C2×#103—431no—
112C2×#103—431no—
113C2×C4×C8—431no—
114C4×C4⋊C4—431no—
115#340—431no—
116#340D4311yescharacteristic
117C43C4×#10311yescharacteristic, complemented, Sylow
118C22×Q8—431no—
119C22×C8—431no—
120C22×C8C2×D4311yescharacteristic
121C4×Q8—434no—
122C4×Q8—862no—
123C2×C4⋊C4—431no—
124C2×C4⋊C4—861no—
125C2×C4⋊C4C2×D4311yescharacteristic
126C2×C4⋊C4C2×D4311yescharacteristic
127C2×C42—431no—
128C2×C42—861no—
129C2×C42—861no—
130#103—434no—
131#103—434no—
132C4×C8—862no—
133#95—861no—
134C2×Q8—432no—
135C2×Q8—432no—
136C2×Q8—432no—
137C2×Q8—861no—
138C2×Q8—861no—
139C2×Q8—861no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—431no—
143C22×C4—431no—
144C22×C4—861no—
145C22×C4—861no—
146C22×C4C22×D4311yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—432no—
150C2×C8—861no—
151C2×C8—861no—
152C2×C8C4×D4312yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—432no—
156C4⋊C4—864no—
157C4⋊C4—861no—
158C4⋊C4C4×D4312yes—
159C4⋊C4C4×D4312yes—
160C42—432no—
161C42—432no—
162C42—864no—
163C42—1722no—
164C23D4×D4311yescharacteristic
165Q8—434no—
166Q8—862no—
167Q8—862no—
168Q8—862no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—432no—
176C2×C4—432no—
177C2×C4—432no—
178C2×C4—432no—
179C2×C4—862no—
180C2×C4—862no—
181C2×C4—862no—
182C2×C4—861no—
183C2×C4—861no—
184C2×C4—862no—
185C2×C4—1721no—
186C2×C4—1721no—
187C2×C4C2×C4×D4311yescharacteristic
188C2×C4C2×C4×D4311yescharacteristic
189C2×C4C2×C4×D4311yescharacteristic
190C2×C4D4×D4311yescharacteristic
191C2×C4#1062190011yescharacteristic
192C2×C4#1062190211yescharacteristic
193C8—22no—
194C8—862no—
195C22C22⋊C4×D4311yescharacteristic
196C22(C22⋊D43)⋊C411yescharacteristic
197C22#1306328711yescharacteristic
198C22SD16×D4311yescharacteristic
199C22Q16×D4311yescharacteristic
200C22#1306334411yescharacteristic
201C22#1306334611yescharacteristic
202C4—42no—
203C4—42no—
204C4—434no—
205C4—862no—
206C4—864no—
207C4—1722no—
208C4C42×D4311yescharacteristic
209C4#1306328311yescharacteristic
210C4(C22⋊D43)⋊C411yescharacteristic
211C4#1306328711yescharacteristic
212C2#1458274611yescharacteristic
213C2#103×D4311yescharacteristic
214C2#1458289211yescharacteristic
215C2#1458298611yescharacteristic
216C2#1458299011yescharacteristic
217C2#1458299111yescharacteristic
218C2#1458299311yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC4×C43C2×C42
FrattiniC22×C4C22×D43
FittingC43×#340C2
socleC23×C43C2×D4
hypercenter#340D43
hypocenterC43C4×#103
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
11. #13063290C4semidirect
17. #13063250C4semidirect
18. #13063248C4semidirect
82. Dic86C42semidirect
101. Dic43#103semidirect
117. C43C4×#103semidirect